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The tight trends (transforms) between two rock physical properties obtained in the physical or digital laboratory on cm- or mm-sized samples may hold for a composite constructed of these samples. One requirement is that all the elements of the composite obey the same trend. Another requirement is that the composite is spatially uncorrelated and, hence, approximately isotropic. The final requirement is that the underlying elemental transforms are approximately linear. The methods we use to address this exportability of trends for the dynamic elastic moduli (or the elastic-wave impedance) versus porosity, permeability versus porosity, and electrical resistivity versus porosity are, respectively, theoretical elastic bounding, numerical reservoir-scale fluid flow, and electrical current simulations. A practical implication is that if an elastic property of a large volume is determined from remote sensing, be it seismic or cross-well data, its average porosity can be estimated using the transforms established at a much smaller scale. Then, this average porosity can be translated into the hydraulic and electrical properties once again, using the elemental transforms established in the physical or digital laboratory. [ABSTRACT FROM AUTHOR]

We tested computational benchmarking data for the absolute permeability, electrical formation factor, and elastic moduli based on the Finney pack, a physical dense random pack of identical spheres digitally rendered into a 3D rectangular coordinate system, as the starting digital object. It is altered by (a) changing the radius of each sphere and (b) geometrically inverting these new packs by swapping grains and pores. Porosity, the absolute permeability, electrical formation factor, and elastic moduli are computed for all these alterations. The direct (grain-based) objects are relevant to clastic rock, and the inverse objects are proxies for carbonates with moldic pores. To corroborate these computational results, we matched the permeability versus porosity, formation factor versus porosity, and elastic moduli versus poros- ity Wends they form by established theoretical rock physics models. These trends persisted when we reduced the scale of investigation by subsampling some of the digital objects under examination. [ABSTRACT FROM AUTHOR]

The objective of this study was to establish a rock physics model of North Sea Paleogene greensand. The Hertz-Mindlin contact model is widely used to calculate elastic velocities of sandstone as well as to calculate the initial sand-pack modulus of the soft-sand, stiff-sand, and intermediate-stiff-sand models. When mixed minerals in rock are quite different, e.g., mixtures of quartz and glauconite in greensand, the Hertz-Mindlin contact model of single type of grain may not be enough to predict elastic velocity. Our approach is first to develop a Hertz-Mindlin contact model for a mixture of quartz and glauconite. Next, we use this Hertz-Mindlin contact model of two types of grains as the initial modulus for a soft-sand model and a stiff-sand model. By using these rock physics models, we examine the relationship between elastic modulus and porosity in laboratory and. logging data and link rock-physics properties to greensand diagenesis. Calculated velocity for mixtures of quartz and glauconite from the Hertz-Mindlin contact model for two types of grains are higher than velocity calculated from the Hertz-Mindlin single mineral model using the effective mineral moduli predicted from the Hill's average. Results of rock-physics modeling and thin-section observations indicate that variations in the elastic properties of greensand can be explained by two main diagenetic phases: silica cementation and berthierine cementation. These diagenetic phases dominate the elastic properties of greensand reservoir. Initially, greensand is a mixture of mainly quartz and glauconite; when weakly cemented, it has relatively low elastic modulus and can be modeled by a Hertz-Mindlin contact model of two types of grains. Silica-cemented greensand has a relatively high elastic modulus and can be modeled by an intermediate-stiff-sand or a stiff-sand model. Berthierine cement has different growth patterns in different parts of the greensand, resulting in a soft-sand model and an intermediate-stiff-sand model. [ABSTRACT FROM AUTHOR]

To validate the transport (fluid and electrical) and elastic properties computed on CT scan pore-scale volumes of natural rock, we first contrast these values to physical laboratory measurements. We find that computational and physical data obtained on the same rock material source often differ from each other. This mismatch, however, does not preclude the validity of either of the data type -- it only implies that expecting a direct match between the effective properties of two volumes of very different sizes taken from the same heterogeneous material is generally incorrect. To address this situation, instead of directly comparing data points generated by different methods of measurement, we compare trends formed by such data points. These trends include permeability versus porosity; electrical formation factor versus porosity; and elastic moduli (elastic-wave velocity) versus porosity. In the physical laboratory, these trends are generated by measuring a significant number of samples. In contrast, in the computational laboratory, these trends are often hidden inside a very small digital sample and can be derived by subsampling it. Hence, we base our validation paradigm on the assumption that if these computational trends match relevant physical trends and/or theoretical rock physics transforms, the computational results are correct. We present examples of such validation for clastic and carbonate samples, including drill cuttings. [ABSTRACT FROM AUTHOR]

Rock physics has evolved to become a key tool of reservoir geophysics and an integral part of quantitative seismic interpretation. Rock-physics models adapted to site-specific deposition and compaction help extrapolate rock properties away from existing wells and, by so doing, facilitate early exploration and appraisal. Many rock-physics models are available, each having benefits and limitations. During early exploration or in frontier areas, direct use of empirical site-specific models may not help because such models have been created for areas with possibly different geologic settings. At the same time, more advanced physics-based models can be too uncertain because of poor constraints on the input parameters without well or laboratory data to adjust these parameters. A hybrid modeling approach has been applied to siliciclastic unconsolidated to moderately consolidated sediments. Specifically in sandstones, a physical-contact theory (such as the Hertz-Mindlin model) combined with theoretical elastic bounds (such as the Hashin-Shtrikman bounds) mimics the elastic signatures of porosity reduction associated with depositional sorting and diagenesis, including mechanical and chemical compaction. For soft shales, the seismic properties are quantified as a function of pore shape and occurrence of cracklike porosity with low aspect ratios. A work flow for upscaling mterbedded sands and shales using Backus averaging follows the hybrid modeling of individual homogenous sand and shale layers. Different models can be included in site-specific rock-physics templates and used for quantitative interpretation of lithology, porosity, and pore fluids from well-log and seismic data. [ABSTRACT FROM AUTHOR]

We offer an effective-medium model for estimating the elastic properties of high-porosity marine calcareous sediment and diatomite. This model treats sediment as a pack of porous elastic grains. The effective elastic moduli of the porous grains are calculated using the differential effective-medium (DEM) model, whereby the intragranular ellipsoidal inclusions have a fixed aspect ratio and are filled with seawater. Then the elastic moduli of a pack of these spherical grains are calculated using a modified (scaled to the critical porosity) upper Hashin-Shtrikman bound above the critical porosity and modified lower (carbonates) and upper (opal) Hashin- Shtrikman bounds below the critical porosity. The best match between the model-predicted compressional- and shearwave velocities and Ocean Drilling Program (ODP) data from three wells is achieved when the aspect ratio of intragranular pores is 0.5. This model assigns finite, nonzero values to the shear modulus of high-porosity marine sediment, unlike the suspension model commonly used in such depositional settings. The approach also allows one to obtain a satisfactory match with laboratory diatomite velocity data. [ABSTRACT FROM AUTHOR]